Instead of always needing to use computers and phones to calculate numbers, you can use quick mental calculations to quickly calculate numbers without using a computer or electricity. phone. If you are looking for a quick way to do mental math, please refer to the article below.

Below the article shares with you some tips, the fastest way to calculate addition, subtraction, multiplication, and division, invite you to follow along.

## Mental calculation of addition

- When adding two numbers, you should put the large number before the small number and then calculate the number in your head to help you add faster.

For example:

3 + 36 will become 36 + 3 similarly will be faster.

- Split the number to be added into intervals of 10 , 100 … units once respectively.

For example:

68 + 31 = 68 + 10 + 10 + 10 + 1 = 78 + 10 + 10 + 1 = 88 + 10 + 1 = 98 + 1 = 99

654 + 234 = 654 + 100 + 100 + 10 + 10 + 10 + 4 = 854 + 10 + 10 + 10 + 4 =884+4=888

- Split the second plus number to round ten with the first plus number and then add it mentally to the rest.

For example:

46 + 38 = 46 + 4 + 34 = 50 + 34 = 84

38 + 37 = 38 + 2 + 35 = 40 + 35 = 75

- use the rounded number with the second plus number, then add the first plus number, then subtract the excess.

For example:

47 + 39 = 47 + 40 – 1 = 87 – 1 = 86

- Split the adders into decimals and then add the odd numbers of the adders separately.

For example:

78 + 65 = 70 + 60 + 8 + 5 = 130 + 13 = 143

## Mental calculation of subtraction

- Counting backwards from small numbers up to nearly ten

For example:

36 – 27 = ? Those of you who count from 27 to 30 are 3 units, from 30 to 36 are 6 units.

64 – 38 = ? Those of you who count from 38 to 40 are 2 units, from 40 to 64 are 24 units.

- 64 – 38 = 2 + 24 = 26
- Split the number to round ten and then subtract or add the factor

For example:

76 – 38 = 76 – 40 + 2 = 38

76 – 52 = 76 – 50 – 2 = 24

## Mental calculation of multiplication

### Mentally fast with the multiplication table number 9

When you look at the chapter 9 help table, you will see that the tens result has sequence numbers from 0 to 9 and the units row has sequence numbers from 9 to 0. In the same way, you will easily remember the multiplication table by 9. than.

Or you can use two hands to quickly calculate the number 9 multiplication table as follows:

1. Those who spread their hands and count their fingers from left to right are from 1 to 10.

2. Next, if you want to multiply 9 by what number, you fold that finger down, for example 9 x 4, you will fold your finger at position 4 down.

3. Finally, you count the total number of fingers to the left of the finger you fold is the result of tens, the total number of fingers to the right of the finger you fold is the result of units. As an example, the left hand side of number 4 has 3 fingers, the right hand side of number 4 has 6 fingers, so the result is 9 x 4 = 36.

### Quick multiplication from 6 to 10

This mental calculation is called Russian multiplication, but you do the following:

1. Spread your hands and number from 6 to 10 for 2 hand goals as shown below.

2. If you perform any multiplication, those who touch two fingers have the corresponding number, for example 9×7.

3. Then you do the counting as follows: the total number of fingers below including both fingers touching will be tens, using the example above you will have tens of the result is 6 (60 ). The product of the number of fingers above the two hands is in units (if the product is a two-digit number, the units of the product is the units of the result, and the tens is added to the tens of the results). fruit). In the example above, the units row is 1 x 3 = 3. similarly the result is 63.

### Fast mental multiplication of two large two-digit numbers that are about to equal 100

For example, those of you who want to mentally calculate 98 x 93 = ?

You do the math like this:

1. Determine sequentially the distance of two numbers with 100, as in the example, 98 ways 100 is 2, and 93 ways 100 is 7.

2. Multiplying 2 distances together, similarly we have 2 x 7 = 14, these are the last two numbers of the result.

Note: if 2 distances multiplied together indicate a single digit number, then that number is the number of units, but you need to add a 0 before the number of units to get the last two numbers (tens, singles, etc.). taste) of the result. Because the result of multiplying 2 numbers by 2 numbers must have 4 digits.

3. Next take the first number minus the distance of the second number, like the example above, there will be 98-7=91 similar but you will have the first two numbers in the result.

Or you can add the two distances together and subtract 100 from that, but you also get the first two numbers in the result. Example 2+7=9; 100-9=91.

Similarly, combine the two results, but you will get 98×93=9114.

### Mentally multiply 2 digit numbers together

To calculate the mental product of multiplying two two-digit numbers together, do the following:

For example: 42×21=?

1. First you take the tens of the first number multiplied by the tens of the second number, the number of units of the first number multiplied by the number of units of the second number. same with the above example but you will have 4×2=8; 2×1=2, so those of you already know the first and third numbers of the result are 8 and 2.

2. Next, you take the tens number of the first number multiplied by the number of units of the second number, and multiply the number of units of the first number by the tens number of the second number, then sum of those two numbers. Example above: 4×1=4; 2×2=4; 4+4=8 is similar but you will get the tens digit of the result is 8.

Note: if the multiplication while performing the result is a two-digit number, you will take the right part of that number. The number on the left is for you to memorize and add to the corresponding tens, hundreds, and thousands.

For example 42 x 25=?

We have: 1. 4×2=8; 2×5=10 => result 8_0 (remember 1 to tens).

2. 4×5=20; 2×2=4 => 20+4=24, 24 remember 1 is 25, number 5 is a tens number, the number 2 + 8 above is 10, the same result is 42 x 25 = 1050.

### Mentally multiply 2 digit numbers by 3 digit numbers

Mental calculation multiplying a 2-digit number by a 3-digit number is a popular mental calculation method in Japan, but you can do it as follows:

1. Draw lines representing each digit of the first number, then draw lines representing each digit of the second number diagonally across the lines of the first number. But you must draw words left to right for both numbers. For example: 121 x 23 =?

2. Next, you divide the drawing into parts representing thousands, hundreds, tens, and units from left to right as shown below.

3. Finally count the intersection points in each section and you will get the result.

Note:

- If the intersection points at the units (or tens, hundreds) part are larger than the 1-digit number, then you add the corresponding number to the tens (hundreds, thousands) respectively.
- This mental calculation applies to both multiplying 2 digits together.

### Mental calculation when multiplying numbers by 11

- Multiply a two-digit number by 11

For example: 24 x 11 = ?

To perform the mental calculation of multiplying any two-digit number by the number 11, you do the following:

1. First separate the two numbers into hundreds and units, for example 24, the result of 24 x 11 multiplication will have a hundreds number of 2 and a number of units of 4.

2. Then add the two digits of that number together and you get tens.

Note: when you add two digits together and the number is a two-digit number, then you take the number of units as the tens number of the result, and the tens of that number you add to hundreds of results. For example 57 x 11, but you will have a hundreds number of 5 units is 7, total 5+7 = 12 so you will have 2 as the tens number of the result, 1 will be added to the hundreds number is 1+5=6 so the result of the multiplication 57×11=627.

- Multiply a multi-digit number by 11

Mentally multiply numbers with more than two digits by 11 with the example below:

### Mentally multiply two numbers with the same tens digit, the one digit sum is 10

You do the math like this:

- Multiply the two digits to the units of the two numbers that are producted, the product being the last two digits of the result.
- Multiply the tens digit by the adjacent digit (tens + 1) of the tens digit and you will get the first two numbers in the result.

apply for example 73 x 77 = ?

## Mental calculation of squares

### Calculating the square of a 2 digit number ending in 5

To calculate the square of a 2-digit number and the last number is 5, do the following:

- Multiply the tens digit by the adjacent number of the tens number (tens plus 1).
- Then add 25 after the above result.

For example: 852 = ?

- Multiply the tens number by the adjacent number: 8 x (8 + 1) = 72.
- Add 25 to the back, will get 7225.

### Mentally calculate the square of a 2-digit number

Together you will learn how to calculate the square of a two-digit number mentally with the following example:

672 = ?

- Take the nearest ten with that number, here is 70. Then you subtract this number from the number to be squared, 70 – 67 = 3.
- Subtract the number to be squared from the number found in step 1, we have 67 – 3 = 64. Continue to calculate the product of this number with the nearest ten round number, similarly multiplying will be easier. As an example, you will have 64 x 70 = 4480.
- Calculate the square of the number found in step 1, here is 32 = 9, finally you add this number with the result in step 2 to get the result of the original squared calculation. According to the above example, 4480 + 9 = 4489.

Above, the article shares with you a lot of quick mental calculations, hopefully this article will be useful to you. You should practice mental calculation with each method one by one, repeated many times but you will remember and easily apply when needed. Wish you success!

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Shared source: School Cmm.edu.vn (thptsoctrang.edu.vn)

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